It seems that you uploaded an image of a geometric sequence assignment. I'll extract and solve the problems for you based on the content.

From the image:

Task:

You are asked to:

1. Find the common ratio of each geometric sequence.
2. Find the next term of the sequence.

Let's go through each sequence in detail:

Sequences provided:

1. Sequence A:
   $5, 15, 45, \dots$

2. Sequence B:
   $10, 2, 0.4, \dots$

3. Sequence C:
   $625, 125, 25, \dots$

4. Sequence X:
   $\frac{1}{2}, \frac{1}{4}, \frac{1}{8}, \dots$

5. Sequence Y:
   $4, -8, 16, \dots$

6. Sequence Z:
   $\frac{3}{4}, \frac{9}{16}, \frac{27}{64}, \dots$

Now, I'll compute the common ratio and the next term for each sequence.

1. Sequence A: $5, 15, 45, \dots$

• Common ratio $r = \frac{15}{5} = 3$.
• Next term: $45 \times 3 = 135$.

2. Sequence B: $10, 2, 0.4, \dots$

• Common ratio $r = \frac{2}{10} = 0.2$.
• Next term: $0.4 \times 0.2 = 0.08$.

3. Sequence C: $625, 125, 25, \dots$

• Common ratio $r = \frac{125}{625} = \frac{1}{5}$.
• Next term: $25 \times \frac{1}{5} = 5$.

4. Sequence X: $\frac{1}{2}, \frac{1}{4}, \frac{1}{8}, \dots$

• Common ratio $r = \frac{\frac{1}{4}}{\frac{1}{2}} = \frac{1}{2}$.
• Next term: $\frac{1}{8} \times \frac{1}{2} = \frac{1}{16}$.

5. Sequence Y: $4, -8, 16, \dots$

• Common ratio $r = \frac{-8}{4} = -2$.
• Next term: $16 \times -2 = -32$.

6. Sequence Z: $\frac{3}{4}, \frac{9}{16}, \frac{27}{64}, \dots$

• Common ratio $r = \frac{\frac{9}{16}}{\frac{3}{4}} = \frac{3}{4} \times \frac{4}{3} = \frac{3}{4}$.
• Next term: $\frac{27}{64} \times \frac{3}{4} = \frac{81}{256}$.

Would you like a deeper explanation of any particular sequence?

Here are five related questions to deepen your understanding:

1. How can you determine if a sequence is geometric?
2. What are the properties of geometric sequences?
3. Can geometric sequences have negative common ratios?
4. How can you apply geometric sequences in real-world problems?
5. What is the general formula for the $n$-th term of a geometric sequence?

Tip: In geometric sequences, multiplying by the common ratio always yields the next term, so if the ratio is fractional, the terms decrease.